•Tigray's ruling party, which is locked in a conflict with Ethiopia's federal government, had threatened an attack.
•The party's forces fired rockets earlier at another region of Ethiopia.
Rockets have been fired from the restive Tigray region of Ethiopia across the border at the capital of Eritrea, local media and diplomats say.
Explosions were heard in Asmara as several rockets landed on the outskirts of the city but there were no immediate reports of injuries.
Tigray's ruling party, which is locked in a conflict with Ethiopia's federal government, had threatened an attack.
The party's forces fired rockets earlier at another region of Ethiopia.
The Tigray People's Liberation Front (TPLF) said it had targeted two sites in the Amhara region on Friday and warned of further strikes.
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Ethiopia has been through big changes since its prime minister Abiy Ahmed came to power in 2018. He was awarded the Nobel peace prize last year after reaching out to make peace with neighbouring Eritrea, with whom Ethiopia had fought a bloody war two decades ago.
But the widespread reforms he pushed through sidelined the Tigrayans of the TPLF who had long dominated the political scene - and in recent weeks, tensions between the TPLF and the federal government seriously escalated.
Fighting over Tigray has also affected Sudan, with at least 17,000 civilians crossing the border from Ethiopia, according to the UN.
What happened in Eritrea?
On Saturday night, residents of Asmara reported hearing loud explosions, amid reports of rockets landing near the city's airport.
The Tigrayans had earlier threatened missile strikes against Eritrea, having accused its forces of crossing into Ethiopia to back federal forces there.
While Eritrea's government has denied any role in the conflict, the BBC's Africa regional editor Will Ross says reports of fighting along the border, and of soldiers being treated in Eritrean hospitals, suggest the opposite is true.
Analysis: Two men with a common enemy
With missiles being fired into Eritrea this conflict has now become far more serious and is likely to be harder to stop. The repercussions could now cause instability in the whole region.
But many people familiar with recent political developments had predicted trouble was brewing when Ethiopia's Prime Minister Abiy Ahmed became a strong ally of Eritrea's authoritarian leader, Isaias Afwerki.
Now the two men have a common enemy - the Tigrayan politicians of the TPLF who dominated Ethiopia's political scene for years, including the time when Ethiopia and Eritrea fought a border war that left tens of thousands dead.
International calls for dialogue have so far been ignored and thousands of civilian refugees continue to flee the fighting into Sudan.
What do we know about Friday's attacks?
Late on Friday, rockets were said to have been fired towards the cities of Bahir Dar and Gondar, in the state of Amhara - whose forces have been fighting with the federal government's against Tigray.
One rocket hit the airport in Gondar and partially damaged it, while a second fired simultaneously landed just outside of the airport in Bahir Dar, an Ethiopian government official said.
The Tigrayans said the rocket attacks were retaliation for recent air strikes conducted by Mr Abiy's forces.
"As long as the attacks on the people of Tigray do not stop, the attacks will intensify," spokesman Getachew Reda said in a Facebook post.
Ethiopia's prime minister has predicted a swift military victory in Tigray, but he may have underestimated his enemy, says our regional editor.
Tigrayan troops are experienced and know the mountainous terrain well, he says. There are fears that a drawn-out regional conflict would have dire consequences for civilians in Ethiopia and the wider Horn of Africa.
How bad is the violence?
Hundreds have died in Ethiopia since the fighting began, with reports of a civilian massacre emerging this week.
Human rights group Amnesty International said it had confirmed that "scores, and likely hundreds, of people were stabbed or hacked to death" in the town of Mai-Kadra (May Cadera) on Monday.
Prime Minister Abiy Ahmed has accused forces loyal to Tigray's leaders of carrying out the mass killings, while the TPLF has denied involvement. Ethiopia's human rights commission said it would send a team to investigate.
What is life like in Tigray?
Communication is difficult at the moment because internet and mobile phone services have been cut.
There are already reports of a shortage of flour and fuel - and, worst of all, water, which was already rationed.
In Mekelle, which has a population of between 400,000 and 500,000, homes used to get piped water once a week, but the supply has stopped.
Families used to buy water from vendors but with phones disconnected they can no longer call to put in orders.
On Thursday it was reported that a power-generating dam had been damaged in an air strike, cutting electricity supply in the region.
I am anxious about the safety of my family, especially my 11-year-old brother who is suffering from cerebral palsy and epilepsy.
I am extremely worried about whether he will get his medication.
As he cannot talk, I used to see him during video calls but that is now not possible.
Why are the government and TPLF fighting?
The TPLF dominated Ethiopia's military and political life for decades before Mr Abiy took office in 2018 and pushed through major reforms.
Last year, Mr Abiy dissolved the ruling coalition, made up of several ethnically based regional parties, and merged them into a single, national party, which the TPLF refused to join.
The feud escalated in September, when Tigray held a regional election, defying a nationwide ban on all polls imposed because of the coronavirus pandemic. Mr Abiy responded by calling the vote illegal.
Tigray's administration sees Mr Abiy's reforms as an attempt to hand his central government more power and weaken regional states.
It also resents what it calls the prime minister's "unprincipled" friendship with Eritrean President Isaias Afwerki.
Mr Abiy won the Nobel Peace Prize in 2019 for his efforts to bring peace with Eritrea.
The prime minister believes TPLF officials are undermining his authority.
Mr Abiy ordered the military operation against the TPLF after he said its fighters had crossed "the last red line". He accused them of attacking a military camp hosting federal troops on 4 November, calling the action "treasonous". The TPLF has denied attacking the camp.