(Adds U.S. State Department comment; paragraph 16)
By Marco Aquino and Mitra Taj
LIMA, March 23 (Reuters) - Peru's new President Martin Vizcarra promised to fight corruption "at any cost," two days after his predecessor was toppled by a sprawling graft scandal and constant clashes with the opposition-run Congress.
As the outgoing president's former vice president, Vizcarra said he would form a completely new cabinet but asked for all lawmakers to help him restore the public's trust in institutions, which had been damaged by the political crisis.
"Enough," said Vizcarra, a former governor of a small mining region, as he began his inauguration speech to Congress.
"We have the obligation to respond to the needs, demands and aspirations of all Peruvians, and not get tangled in a bitter struggle that does enormous damage to Peru."
Vizcarra took office as a scandal involving Brazilian construction conglomerate Odebrecht continued to roil one of Latin America's most stable markets and the world's No. 2 producer of copper.
On the eve of his swearing-in, thousands of protesters marched through downtown Lima to demand early elections, in hopes of purging a political class widely seen as corrupt.
"Out with them all," protesters chanted, before police fired tear gas to disperse crowds.
Former President Pedro Pablo Kuczynski, whom Vizcarra replaces, offered to step down this week in the face of near-certain impeachment over his ties to Odebrecht.
He blamed his downfall on the rightwing party, Popular Force, that won a majority of congressional seats despite losing the presidency in 2016.
Like Kuczynski, Popular Force and its leader, twice-defeated presidential candidate Keiko Fujimori, are also under investigation in connection with Odebrecht and deny wrongdoing.
Vizcarra said Peru's justice system must act independently and swiftly to sort the guilty from the innocent, and warned that no branch of government should trample another.
Since serving as the country's ambassador to Canada for the past six months, Vizcarra has largely steered clear of Kuczynski's troubles, which culminated with vote-buying allegations as Kuczynski's allies scrambled to keep him from being impeached.
But Vizcarra, whom most Peruvians could not name in a poll two weeks ago, must now repair relations with Congress while refocusing the government on its stalled plans, such as building sorely-needed infrastructure and housing in a region hit by severe flooding more than a year ago.
Next month, Vizcarra will face nationwide doctor and teacher strikes and welcome Donald Trump to Peru on the U.S. president's first visit to Latin America for a gathering of the region's leaders that Peru is hosting.
The theme of this year's Summit of the Americas' event in Lima is "democratic governance against corruption."
The United States said it looked forward to working with Vizcarra. "Peru's adherence to its constitution during this transition reflects its strength as a resilient democracy," said State Department spokeswoman Heather Nauert.
Vizcarra, 55, was a civil engineer and governed Moquegua in southern Peru before he teamed up with Kuczynski for the 2016 presidential ticket. (Reporting by Marco Aquino and Mitra Taj; Editing by Richard Chang and Clarence Fernandez)