By Ayesha Rascoe

WARSAW, Poland (Reuters) - President Barack Obama on Friday made an impassioned plea for the nation to do more to address the combative relationship between local police forces and the black and Hispanic communities they serve, after the shootings of two black men by police in Minnesota and Louisiana in two days.

"When incidents like this occur, there's a big chunk of our fellow citizenry that feels as if because of the color of their skin they are not being treated the same," Obama said shortly after landing early Friday morning in Warsaw, Poland, for a NATO summit.

"And that should trouble all of us. This is not just a black issue. It's not just a Hispanic issue. This is an American issue that we should all care about," he said.

The deaths of Philando Castile at a traffic stop in Falcon Heights, Minnesota, and Alton Sterling outside a convenience store in Baton Rouge, Louisiana, were the latest in a string of shootings that have led to calls for a revamp in the way police interact with the black community.

Citing statistics that show that blacks are more likely to be killed by police officers and receive harsher sentences than their white counterparts, Obama said it is "incumbent on all of us to say we can do better than this."

A White House task force on better policing tactics issued recommendations last year on how to improve community relations with law enforcement.

Obama encouraged local police forces to adopt the practices outlined by the task force, saying that less distrust of police would help to keep officers safe and lead to less deadly shootings by authorities.

Critics of the push to reform local police tactics have charged that Obama has not shown enough concern about police officers who are shot in the line of duty.

Obama repeatedly stressed that he believes that most police officers do their jobs without bias and that addressing complaints about police brutality would not undermine law enforcement.

"When people say black lives matter, that doesn't mean blue lives don't matter. It just means that all lives matter, but right now the big concern is the fact that data shows black folks are more vulnerable to these kinds of attacks," he said.

Earlier on Thursday, Obama issued a Facebook post urging the nation to address the "appearance or reality of racial bias" in policing.

(Reporting by Ayesha Rascoe; Editing by Leslie Adler)