China has called for a cease-fire and put forward a 12-point peace plan that has been criticized by the West.
"We are always open to negotiations," Putin told Xi. "We will certainly discuss all these issues, including your initiatives which we treat with respect, of course."
"We have plenty of common tasks and objectives," Putin said, adding it was "symbolic" that the Chinese leader chose to travel to Russia for the first foreign visit of his new term.
Xi highlighted China's "close ties" with Russia, saying: "We are partners in comprehensive strategic cooperation. It is this status that determines that there should be close ties between our countries."
Putin told Xi that he was "slightly envious" of China´s "very effective system for developing the economy and strengthening the stae."
Xi praised Putin and predicted he would be elected next year.
"Under your strong leadership, Russia has made great strides in its prosperous development," Xi said.
Ukraine's Foreign Ministry said it was "closely" following Xi's visit and urged him to use Beijing's influence to push for an end to the war.
Meanwhile, US Secretary of State Antony Blinken condemned Xi's visit.
“That President Xi is traveling to Russia days after the International Criminal Court issued an arrest warrant for President Putin suggests that China feels no responsibility to hold the Kremlin accountable for the atrocities committed in Ukraine," U.S. Secretary of State Antony Blinken said.
"Instead of even condemning them it would rather provide diplomatic cover for Russia to continue to commit those grave crimes,” he added.
The trip was expected to give Putin a political boost at a time when he is increasingly isolated internationally and has been accused by the ICC of committing war crimes in Ukraine.