The Afghanistan veterans, who fought in the 1979-1989 war under the Soviet Union, are at the frontline behind the barricades on Kiev's Independence Square, which for nearly three months has been occupied by protesters demanding the departure of President Viktor Yanukovych.
These former soldiers have said several times that they want to keep fighting until the end -- or until the end of the current regime.
Klitschko, who watched a documentary with and about the veterans ahead of the anniversary of the Soviet Union's retreat from Afghanistan on Saturday, said he was ready to challenge Yanukovych in a televised debate.
"We do not want to become a cog in the wheel of current authorities, but we are ready to assume our responsibilities, if there is a complete remodelling of these authorities, which have been discredited," he said.
The protest movement erupted in November after authorities rejected a key EU pact in favour of closer ties with Russia.
Yanukovych largely ignored opposition demands until protests turned deadly in January, prompting him to dismiss the unpopular government.
Protesters are waiting for him to announce a new government they hope will be pro-West, and they also want him to step down altogether.
"People have been gathered on the Maidan (square) for nearly three months and authorities are not hearing their requirements... One of the solutions is early presidential elections," he said.
Yanukovych's current mandate expires in March 2015.
"This film has resonance now, as it shows the courage of soldiers enlisted in war, which could be a model for the youth of today," one former fighter said before the start of the film in a Kiev cinema.
Klitschko, whose father was an officer in the Red Army, watched the documentary with a dozen veterans, aged around 50.