The Islamic Courts Union now controls almost all of the country's capital and much of southern Somalia after taking over Mogadishu's main port on Wednesday.
Since gaining control of the port, many Somali militiamen who formerly supported the warlords have offered to surrender their weapons and work with the Islamists.
"We have been working with the warlords for a long time, so now it is time to give the chance (to the Islamic group)", said militia commander Yusuf Iyow on Thursday. "We are committed to forget the past hostilities and to work with them."
"The only power in Mogadishu is the Islamic Courts Union, so there is no other option open for us but to surrender. Defiance only kills people and does not create opportunities" for peace, Iyow said.
The Islamists were set to meet officials from the largely powerless interim government this weekend but the talks have been delayed indefinitely.
Two senior government officials said Sudan - where the Arab-sponsored talks were to have been held - had told them of the postponement but said they did not know why.
"I assume it has something to do with leadership confusion within the Islamic courts," a Somali cabinet minister said.
A cleric in the Supreme Islamic Council of Somalia (SICS) also confirmed the delay but suggested the meeting had been put on hold because the government was not prepared.
The meeting in Khartoum was to have been the second between the two sides. On June 22, they reached a mutual recognition and truce accord at Arab League-mediated talks.
They agreed to meet again on July 15 to further discuss arrangements for security and governing in Somalia but since then the Islamists have expanded their territory leading to claims that they violated the deal.
On Thursday, the United Nations Security Council backed a move to ease the arms embargo on Somalia to allow the possible deployment of foreign peacekeepers.
The move is designed to help the interim government build an effective security force in the country.
The interim government was formed under United Nations supervision in late 2004 but has almost no influence outside its base in Baidoa, 250km northwest of the capital.