Gunfire continued to echo around the city, but Itar-Tass quoted a local television commentator as saying: "The attempted coup has failed".
It quoted the television as saying forces loyal to Nabiyev had agreed to leave the parliament building they seized Saturday morning and government forces had "liberated" other government buildings.
The television said the accord was reached at talks between Akbarsho Iskandarov, acting head of state of the Central Asian republic, and Nabiyev ally Safarali Kenjayev at Dushanbe's Russian Army headquarters.
Itar-Tass said Kenjayev had about 150 unarmed supporters in the parliament and groups of his men were leaving the city, trying to break through lines of government forces.
Hundreds of people have been killed in five months of virtual civil war in the southern Kurgan-Tyube and Kulyab regions south of Dushanbe. The conflict entered a decisive phase this weekend when forces from Kulyab, a stronghold of support for Nabiyev, who was ousted in September by a coalition embracing radical Moslems and parliamentary democrats, entered the capital.
The reported retreat came after a weekend of fighting in Dushanbe.
Rebel forces from the strongly pro-Nabiyev southern Kulyab region had seemed to control the city center on Saturday, but heavy submachine-gun fire and mortar explosions could be heard on the main street, near parliament. Lorries roared through the streets, gunmen leaning from the sides with rifles at the ready.
Buses packed with women, children, furniture and bundles of clothes struggled out of the city.
Interfax said pro-Nabiyev and government forces had agreed during talks at a Russian Army base to an emergency session of parliament in Nabiyev's Leninabad home district, where he has been in exile.
Itar-Tass said that parliamentary leaders had appealed Sunday for deputies to attend Monday's session.
The meeting, to be guarded by Russian soldiers, would consider the legality of the removal of Nabiyev, the former Communist Party leader, who was forced to resign at gunpoint last month.
Russia said it feared "catastrophic consequences" if the conflict, which has killed hundreds since May, spread unchecked through Central Asia. The Foreign Ministry in Moscow called for Commonwealth and United Nations efforts to end the fighting.
"The destiny of Russian citizens", a statement said, "is a matter of particular concern". The wording suggested Russian troops, neutral in the conflict, could be used if the large Russian population became a target.
Russian troops currently guard a number of key installations, including the airport and the city's television center.
Andrei Kozyrev, Russia's foreign minister, called for urgent talks by Russia's Security Council on protecting Russians in Tajikistan.
General Eduard Vorobyov, first deputy commander-in-chief of Russia's ground forces, said Russian military vehicles and an army base in Dushanbe were shelled on Sunday, Itar-Tass reported.
Moscow shares Western countrie's fears that Tajikistan, which has ethnic and linguistic links to neighboring Iran, could swing toward Islamic fundamentalism. Many suspect mujahi-deen leaders in Afghanistan of fueling the conflict, blaming them for arms running across the common frontier.
The United States evacuated its diplomats along with some British and Canadian nationals on a special flight on Sunday morning. A spokesman said they were being brought to a military air base near Frankfurt, Germany.
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