Russia has accused the US of using its aid agency in Moscow to covertly influence the country's politics and elections, explaining its decision to expel the mission amid a wider crackdown on the opposition movement.

The Russian government has given the US agency for international development (USAid) until 1 October to cease all operations in the country. The agency helps fund a number of pro-democracy and human rights groups that have provoked the Kremlin's wrath amid an unprecedented opposition movement against the Russian president, Vladimir Putin.

In an uncharacteristically blunt statement, the Russian foreign ministry said that the decision to shut USAid was taken primarily because the agency's work "does not always correspond to [its] stated goals".

"This means attempts to exert influence, via the distribution of grants, upon political processes, including elections of various levels and institutions of civil society," it said.

Putin has accused the US state department of orchestrating the mass protests that have swept Moscow since he announced his intention to run for the presidency again late last year. A main target of his ire has been Golos, an independent election monitoring group that receives the bulk of its funding from USAid and was key in exposing electoral fraud in a December parliamentary vote that helped bring tens of thousands of protesters on to the streets.

The foreign ministry also expressed its displeasure with the agency's work in the troubled North Caucasus, a region still wracked by the remnants of a violent Islamist insurgency. "USAid's activity in the Russian regions, especially the North Caucasus, prompted serious questions, which we warned our American colleagues about repeatedly," the statement said.

USAid has been operating in Russia since the Soviet Union's collapse, funding groups that have received little or no government support, including medical NGOs devoted to fighting HIV/Aids and tuberculosis and various environmental groups. Yet the bulk of its funding goes to civil society groups focused on building up democracy and human rights in the country, including Golos, human rights NGO Memorial and corruption watchdog Transparency International.

Putin has repeatedly criticised groups that receive foreign funding and has accused opposition protesters of acting on orders from Hillary Clinton, the US secretary of state. The Russian parliament passed a law this summer obliging NGOs that receive foreign grants to publicly brand themselves "foreign agents", a term reminiscent of the spy terminology used during the cold war.

Grigory Melkonyants, the deputy director of Golos, said it was "practically impossible" to get funding from within Russia. "Supporting human rights – be it for prisoners, or election monitoring, or anything – is a very sharp question for our current leadership. Business doesn't want to risk putting money into this," he said.

Putin has taken great pains to convince the wider Russian population that any criticism of his government is a foreign plot. Russian officials and media have also accused the US of being behind the Arab spring uprisings, including in Egypt, where USAid came under pressure in the wake of Egypt's uprising against former president Hosni Mubarak.

The move against USAid was announced by the state department on Tuesday and official state media in Russia remained silent on the issue on Wednesday. An official inside the Obama administration vowed that the US would find ways to continue to fund civil society groups, potentially paving the way for a long stand-off.

The Russian government brought immense pressure against the British Council in the wake of the murder of dissident Alexander Litvinenko in London in late 2006 in a tussle that lasted for more than a year.

The foreign ministry also said its decision to shut USAid was prompted by the "maturity" of its civil society. "Russian civil society has become entirely mature and does not need 'external leadership'," it said.

Government critics said the move was the latest attempt to put pressure on the opposition. In the past few months, charges have been brought against more than a dozen protesters as well as opposition leader Alexei Navalny. Opposition MP Gennady Gudkov was stripped of his mandate last week. A series of laws that increase fines for protesting and slander have been passed, as well as a bill that critics fear will tighten the government's control over the internet.