There have been reports of increasing lawlessness in Kabul
Deposed leader Burhanuddin Rabbani is reported to be due to return soon to Kabul, which has now been taken over by one faction of the Northern Alliance.
But it remains unclear why he has still failed to appear, having been expected in the capital since Wednesday.
Although the United Nations still recognises Mr Rabbani as the country's president, many Afghan groups reject his authority.
UN envoy Francesc Vendrell is also heading for the Afghan capital to coordinate talks this weekend on forming an interim broad-based government.
Old rivalries
A Russian delegation is going there, too, to meet what Defence Minister Sergei Ivanov called "the leadership of the legitimate government" - a clear reference to the Northern Alliance.
Russia continued to recognise the Northern Alliance as the legitimate administration in Afghanistan throughout the years of Taleban supremacy and gave it military assistance.
The BBC Moscow correspondent says Russia is now signalling to the West its determination to secure a dominant role for the Alliance in the post-Taleban leadership.
It is still unclear to what extent the Russian move could put Moscow on a collision course with Washington and other Western countries that want to ensure that the Northern Alliance does not dominate the next government, analysts said.
The coalition against terrorism may pride itself on the relative ease with which the Taleban have been removed from power.
But the fall of Kabul has created a volatile and dangerous situation.
Many mujahideen commanders and tribal leaders do not recognise Northern Alliance authority.
And ethnic rivalries could easily turn elements of the Alliance against each other, rekindling the vicious factional fighting which ripped Kabul apart in the early 1990s.
UN talks
The Alliance is dominated by ethnic Tajiks, like Mr Rabbani, who are Sunni Muslims.
Their Jamiat-i-Islami group is now largely in control of Kabul, and has said there is no need for international peacekeepers.
But several hundred ethnic Hazara troops - minority Shia Muslims persecuted by the Taleban and other previous regimes - are heading for the capital to protect Hazaras and to demand a share in any administration.
Abdul Karim Khalili, head of the Hazara Hezb-i-Wahdat faction, told AFP his troops would not enter Kabul itself.
He said he would station his troops just outside the city and would travel into Kabul himself to meet Mr Rabbani.
The Hazaras are nominally part of the Northern Alliance, but loyalties in Afghanistan shift easily.
Now, there are reports of rising lawlessness in the capital.
The BBC Afghanistan correspondent says ordinary Afghans do not trust the militia leaders, and are desperate for an international military presence.
US diplomacy
The United States envoy to Afghanistan, James Dobbins, has also been holding talks in Pakistan on plans for a transitional government.
He arrived from Rome, where he met Afghanistan's former king, Zahir Shah.
The Northern Alliance previously said it supported the idea of a grand council of elders led by the former king, but now seems to have gone lukewarm on the idea.
As well as competing interests in the Alliance, there are entirely separate factions outside the capital who are now also looking to claim power.
Around the eastern city of Jalalabad, men loyal to Yunus Khalis, a Mujahideen party leader who has been largely silent for years, are now staking a claim in areas where they once fought Soviet troops.
Mr Khalis is not allied to the Northern Alliance, and the re-emergence of such independent operators is being seen as a sign of the factionalism into which Afghanistan could so easily descend again.