MINNEAPOLIS — President Obama declared Monday on his first trip outside Washington to promote gun control that a consensus is emerging for universal background checks for purchasers, though he conceded a tough road lay ahead to pass an assault weapons ban over formidable opposition in Congress.

‘‘We should restore the ban on military-style assault weapons and a 10-round limit for magazines,’’ Obama said in a brief speech in Minneapolis, standing firm on the gun-control measures he favors despite long odds.