WASHINGTON — President Obama declared on Wednesday that he would make gun control a “central issue” as he opens his second term, promising to submit broad new firearm proposals to Congress no later than January and to employ the full power of his office to overcome deep-seated political resistance.

Leading House Republicans responded to the president’s pledge in the aftermath of the Connecticut school massacre by restating their firm opposition to new limits on guns or ammunition, setting up the possibility of a bitter legislative battle and a philosophical clash over the Second Amendment soon after Mr. Obama’s inauguration.

Having avoided a politically difficult debate over guns for four years, Mr. Obama vowed to restart a national conversation about their role in American society, the need for better access to mental health services and the impact of exceedingly violent images in the nation’s culture.

He warned that the conversation — which has produced little serious change after previous mass shootings — will be a short one, followed by specific legislative proposals that he intends to campaign for, starting with his State of the Union address next month.