WASHINGTON — Some Congressional Republicans said Thursday that they would increase their efforts to prevent residents here from possessing small amounts of marijuana, which became legal in Washington at midnight, and warned that the city would face numerous investigations and hearings should the mayor continue her practice of telling them to please find something else to worry about.

“We say move forward at your own peril,” said Representative Jason Chaffetz of Utah, chairman of the House Oversight Committee, echoing a letter he and Representative Mark Meadows, Republican of North Carolina, sent to city officials this week, warning of legal action and ordering the district to turn over documentation on any employees involved with putting the law into effect.