The District of Columbia has defied threats from Congress and moved forward with legalising possession of marijuana after a voter-approved initiative.

Despite last-minute manoeuvres by Republican leaders in Congress and threats that city leaders could face prison time, DC mayor Muriel Bowser said the city was implementing marijuana legalisation as approved by voters. The new law took effect at 12.01am local time.

Ms Bowser, a Democrat, said the city's plans have not changed despite a letter from two leading House Republicans warning of repercussions if the city moves forward with legalisation.

Congress has final say over the laws in the District of Columbia, and the two sides disagree about whether Congress acted quickly enough to block an initiative legalising marijuana, which was approved by nearly two-thirds of city voters in November.

Representative Jason Chaffetz, who chairs the House Oversight Committee, urged Ms Bowser in a letter late on Tuesday to reconsider her plans to implement the initiative, saying that doing so would clearly violate federal law.

"Bullying the District of Columbia is not what his constituents expect, nor do ours," Ms Bowser said. "We do disagree on a matter of law. There are reasonable ways to resolve that without us threatening him or he us."

The District becomes the first place in the US east of the Mississippi River where recreational pot is legal. Alaska also legalised pot this week, joining Colorado and Washington state.

The initiative legalises possession of up to 57g for use at home, and people are also permitted to grow up to three mature plants. Smoking marijuana in public remains illegal, as does buying or selling the drug.