Ministry spokesman Yevhen Perebiynis said the reporter was expected to contact the Ukrainian Embassy in Damascus Tuesday, the British newspaper The Guardian reported.
Kochneva, who has written for Syrian and Russian newspapers, was kidnapped in October and reportedly held by members of the Free Syrian Army opposition group.
Kochneva announced her escape in a blog post, The Guardian said.
"Your Alice has come back through the looking glass. More later," the post read.
In interviews with Russian media, Kochneva said she escaped from the house where she was held and walked about 9 miles before reaching a Syrian army checkpoint.
Kochneva said she would remain in Syria, which is "a friend in need."
"The world is just blind," Kochneva told radio station Business FM. "I will do everything for the people to know what is really going on here."
Syria's highest religious leader, Sheik Ahmad Badr al-Deen Hassoun, a Sunni cleric linked to President Bashar Assad, has called for more Syrian army recruits, The New York Times reports.
Assad's armed forces need more recruits and may begin to enforce required military service laws for the first time since the conflict began two years ago, the Times said.
A Washington think tank said about 40 Syrian soldiers are killed daily, The Guardian reported.
Jeffery White of the Washington Institute, said a study of funeral data by an analyst indicated "the army was exhausting itself."
He said the government has increasingly relied on auxiliary and irregular forces. A U.N. report released Monday said the Syrian government was turning to armed militias.
France urged the European Union to re-examine whether to lift an arms embargo on Syria to help rebels, a position at odds with Germany, which has said such a move could foment regional conflict, The Guardian said.
French Foreign Minister Laurent Fabius said after a European Union meeting Monday in Brussels there is an "imbalance" in the conflict because the Syrian regime is "being supported by heavy weapons coming from Iran and Russia, but the [rebel] National Coalition does not have the same weapons at its disposal," the EUobserver reported.
Reconsidering lifting the embargo must be soon, he said, "because we cannot tolerate this imbalance, which is resulting in the massacre of the entire population."
German Foreign Minister Guido Westerwelle said EU countries should send aid for "infrastructure, medical assistance, electricity, water."
"I don't think the bloodshed in Syria will decrease should we engage in an arms race," Westerwelle said.
Data released by the U.N. refugee agency indicated the number of Syrians registered as refugees or awaiting registration is 1.1 million. The United Nations warned Sunday the number of refugees could reach 3 million this year.
In Washington, the United States condemned the killing of 48 Syrian troops in Iraq as an act of "terrorism" after al-Qaida claimed responsibility.