Mr Putin's Q&A sessions have become something of an annual event in Russia
Russian Prime Minister Vladimir Putin has said he will think about running for president again in 2012.
"I will think about it," said Mr Putin during an annual Q&A session with Russian citizens. He served as Russia's president from 2000 to 2008.
Answering some of 700,000 questions from viewers, he called for tough measures against those behind Friday's train bombing, in which 26 people died.
He said the attack showed the threat to Russia from terrorism remained high.
He also said the US was hindering Russia's efforts to join the World Trade Organisation, adding that his priority was to strengthen relations with Russia's neighbours.
'Break terrorism's spine'
In the wide-ranging Q&A session, Mr Putin condemned last Friday's attack on the Moscow-St Petersburg express train, in which senior government officials were killed.
By Rupert Wingfield Hayes, BBC News, Moscow
Many people were expecting Vladimir Putin to give an indication of who his government thinks was behind last Friday's train attack. Instead they got platitudes.
Was he sorry for the victims and their families? He didn't say. Does his government believe the claims of Chechen separatists that they carried out the attack? We weren't told.
Mr Putin's rambling three-hour broadcasts are an annual event here. When they started eight years ago they were a novelty.
Their seeming spontaneity and Mr Putin's command of facts and figures made them a huge hit. But eight years on, the whole performance is starting to look like very tired propaganda.
A North Caucasus Islamist group has claimed responsibility for the attack on the Nevsky Express, some 400km (250 miles) north-west of Moscow.
"It is necessary to act in a very tough way against criminals who carry out these kinds of terrorist attacks," said Mr Putin.
"We have done a lot to break the spine of terrorism, but the threat has not been fully liquidated... The threat of terrorism remains very high."
He urged viewers to remain vigilant and alert to the possibility of future attacks.
A website claim on Kavkazcenter.com said the train attack was carried out by the "Caucasian Mujahadeen" on the orders of its leader, Doku Umarov.
The Chechen is described as one of Russia's most wanted rebels, but it was not possible to verify the claim's authenticity.
Mr Putin's annual phone-in appearance, which was aired live on state television, recalled similar Q&A sessions during his eight-year presidency.
He stood down after two consecutive terms as president in 2008, but the term in office has since been extended to six years, making him eligible to stand again.
The phone-in was a largely stage-managed event, the BBC's Tom Esslemont reports from Moscow.
Mr Putin's successor as president, Dmitry Medvedev, has not made any such appearances.
Taking questions from around the country, Mr Putin said it was not only security that was at the forefront of people's minds.
One woman appearing by live video-link asked how she should survive the recession. Mr Putin tried to reassure her by saying the worst of the economic crisis was over.
On trade, Mr Putin said: "For some unknown reasons some countries, including the United States, are hindering our accession to the WTO."
The US has said it backs Russia's entry to the 153-member trade organisation, which opens up trade between member states.
But this week US officials said they were concerned about Mr Putin's threat to widen Russia's WTO bid to include its neighbours Belarus and Kazakhstan, with whom it has formed a customs union.
Mr Putin also fielded questions from Togliatti, where Lada is based, voicing his support for the struggling carmaker.
"We must not lose this brand, even if the share of our foreign partners changes," he said.
"A Conversation with Vladimir Putin: The Sequel" was being broadcast from a conference centre next to the Kremlin and lasted for a number of hours.
The eighth session of its kind, the interview has become something of an annual event, and organisers said they had received more than 700,000 questions by phone, text message and through the internet.