The concerns of foul play could tarnish relations between Russia and Western nations, which Putin warned in the campaign to keep their "snotty noses" out of Russian affairs.
"Reports from Russia include that there were allegations of Election Day violations, and we have urged the Russians to look into those," White House spokeswoman Dana Perino said.
"It is vital that the Russian Central Election Commission urgently investigates all allegations of electoral abuses," Britain's foreign ministry said.
Observers from the Council of Europe and the Organisation for Security and Cooperation in Europe (OSCE) described the election as "not fair" in a statement, saying it "failed to meet many ... commitments and standards for democratic elections".
Europe's main ODIHR election watchdog decided not to monitor the election, citing obstruction by Russian authorities.
Opposition parties said one-sided press coverage, heavy use of government resources to campaign for pro-Kremlin parties, and irregularities in voting skewed the outcome.
The Communists, the liberal Union of Right Forces and opposition icon Garry Kasparov have all described the election, in separate comments, as the "dirtiest in Russian history".
The head of Russia's Election Commission, Vladimir Churov, a former colleague of Putin, dismissed the allegations of fraud.
Kremlin spokesman Dmitry Peskov said the vote had been democratic and said it would mean Putin's policies will continue to be implemented after leaving office. "He has got support for the continuation of his course (and) he wants all his projects to be continued," Peskov told reporters.
Projections by the Electoral Commission showed pro-Kremlin parties would win about 393 of the 450 seats in the next State Duma, the lower house of parliament.
That would be more than enough to allow them to change the constitution if they wished, one way which some Putin supporters have suggested would allow the Kremlin chief to remain in command of Russia.
Putin has been careful to give few clues about how power will be handed over to the victor of March elections, provoking intense speculation by investors who have invested billions of dollars since he was first elected in March 2000.
Opinion polls show Putin, a 55-year-old former KGB agent, is extremely popular after eight years in power. Voters credit him with restoring stability and national pride and like his tough nationalism and criticism of the West.
