The British Foreign Office said: "The Government is concerned about allegations of electoral malpractice which, if proven correct, would suggest that the Russian elections were neither free nor fair... It is vital that the Russian Central Election Commission urgently investigates all allegations of electoral abuses."
Echoing the statement French Foreign Ministry spokesman Pascal Andreani noted numerous reports of violations and demanded that "the Russian authorities shed light on the accusations."
Top international observers said on Monday that Russia's elections, which saw a landslide victory for President Vladimir Putin's party, had failed to meet basic democratic standards. They said Putin, who headed United Russia's candidate list and proactively campaigned on its behalf, had effectively merged the state with his party in the run-up to the election.
"Merging of the state and a political party is an abuse of power and clear violation of international standards," Goran Lennmarker, head of the OSCE's Parliamentary Assembly told reporters in Moscow.
Washington said on Sunday it was concerned about the use of state administrative resources in United Russia's favor and called on Russian authorities to investigate reports of abuse.
Other violations cited by the Organization for Security and Co-operation in Europe (OSCE) and the Council of Europe included a higher party threshold, the abolishment of the "against all" option and of the minimum voter turnout requirement, and pressure on the opposition.
Russia's opposition has also claimed the polls were rigged, and some voters were either intimidated into voting for the ruling party or induced to cast their ballots for it. And Communist leader Gennady Zyuganov said the vote had been rigged "in 20 different ways" and pledged to challenge the results.
Monitors from the Commonwealth of Independent States (CIS), a group of ex-Soviet states, said however the elections had been free and fair.
With 98% of Sunday's vote counted, preliminary results give the United Russia party 64.1%, the Communists 11.6%, the ultranationalist Liberal Democratic Party 8.2%, and the loyalist A Just Russia 7.8%.
Putin himself said in a televised statement on Monday the elections were a demonstration of confidence in his rule, and they showed that Russians would not allow a rollback of their country into the chaos of the 1990s.
Foreign media reports highlighted an improbably high turnout in Russia, especially in Chechnya, where President Ramzan Kadyrov claimed that 99% of the population had voted.
The Times said "United Russia had turned the election into a referendum on his popularity as part of a plan to declare him the 'national leader.'"
Putin will step down as president after two years in office. Continuing to enjoy high popularity ratings, he has repeatedly said he will not breach the Constitution to run for a third term, but has said good results for United Russia will give him the "moral right" to retain power.