MOGADISHU, Somalia — Somalia government soldiers, joined by troops from neighboring Ethiopia, advanced toward Somalia’s capital yesterday as Islamic fighters dug in and promised a “new phase” in the war — a chilling pronouncement from a movement that has threatened suicide attacks.

Somalia called on the Council of Islamic Courts militias, bloodied by a week of artillery and mortar attacks, to surrender and promised amnesty if they lay down their weapons, government spokesman Abdirahman Dinari said.

A U.N. official, meanwhile, said yesterday that Ethiopian-backed government troops were advancing on Mogadishu, the capital, from two directions and facing stiff resistance.

Francois Lonseny Fall, the top U.N. envoy to Somalia, also said 35,000 Somalis had crossed into neighboring Kenya to escape the fighting, which forced the United Nations to suspend aid delivery to two million Somalis.

As many as 1,000 people may have been killed and 3,000 wounded in the fighting, many of them foreign radicals, Prime Minister Meles Zenawi of Ethiopia said.

Mr. Meles said about 3,000 to 4,000 Ethiopian forces, which entered Somalia on Saturday, may soon wrap up their offensive against the Islamic militias that until recent days controlled most of southern part of the country.

“As soon as we have accomplished our mission — and about half of our mission is done, and the rest shouldn’t take long — we’ll be out,” Mr. Meles told reporters in the Ethiopian capital, Addis Ababa.

Mr. Fall called the fighting “disastrous” for the Somali people and asked the Security Council for an immediate cease-fire. But diplomats said it was unlikely the council would act soon.

A U.S. State Department spokesman in Washington appeared to endorse Ethiopia’s military action, saying it had “genuine security concerns” about the growth of powerful Islamic militias.