According to the radical Islamist group, Al Shabaab, the arrival of Ethiopian troops in Somalia is a sign that the Kenyan military operation against them is failing.
The Kenyan military said warplanes backed by salvoes from warships off Somalia's coast destroyed an al Shabaab training camp in the Hola Wajerer/Lacta area of the Babade district.
An al Shabaab spokesman told Reuters the air strikes had landed in empty bush where they now had no bases.
The Kenyan assault on al Shabaab appeared to have slowed this week before the move by Ethiopia with Kenya blaming heavy rains and mud. Al Shabaab says guerrilla-style attacks have halted the advance.
Scores of Ethiopian military vehicles, ferrying troops and weapons, pushed at least 80 km (50 miles) into Somalia on Saturday, according to local residents and elders, crossing into the centre of the near-lawless country from Ethiopia and travelling through Kenya to reach its south.
Ethiopia on Sunday continued to publicly deny that any of its forces had entered its Horn of Africa neighbour.
Residents and elders witnessed the convoys and identified them to Reuters as Ethiopian. Al Shabaab also reported the presence of Ethiopian forces in several towns.
An Ethiopian Foreign Ministry spokesman said no decision had yet been made on whether to support the Kenyan army, which entered Somalia five weeks ago vowing to wipe out al Shabaab, who it blames for kidnapping and attacking tourists on its soil.
"We are glad to say Ethiopian troops are in the Guriel area. They have come because AMISOM and Kenya have failed in the fight against al Shabaab," Sheikh Abdiasis Abu Musab, an al Shabaab spokesman, told Reuters.
Arm and train
AMISOM is an African Union force of Ugandan and Burundian troops that has been largely responsible for keeping al Shabaab from ousting Somalia's internationally-backed but weak government.
It was unclear what the intentions of the Ethiopians were. Some local elders said they would fight al Shabaab and others that they will arm and train militias loyal to the government.
The last time Ethiopia entered Somalia was in December 2006, with tacit U.S. backing and at the invitation of a government that had lost control of the capital Mogadishu and large swathes of the country to another Islamist group.