"This conversation is a source of optimism to me," Kaczynski told reporters in Warsaw, Poland, after the two met. While acknowledging "some difficulties" remain to be discussed about a missile defense system, the president said, "We hope they will be resolved."
Biden also called the meeting productive.
"I know of no problem of consequence we have with Poland," he said. "I know of no problem that is not able to be resolved as they emerge."
Biden said they discussed "the leading role that Poland can play if it chooses to play" on a defense system to protect Europe from missile attacks by rogue nations.
"And I welcome the president's support for the missile defense, and for Poland's offer to host a standard missile, this so-called SM-3s, in a third stage," Biden said.
The phased approach to missile defense advocated by U.S. President Barack Obama is "a more adaptable, rational and workable system" that will strengthen missile defense in Europe, Biden said.
"Simply put, it's better for NATO, it's better for Poland, it's better for Europe, it's better for the United States," Biden said.
As he did after meeting with Polish Prime Minister Donald Tusk, Biden thanked Poland for deploying its troops to Afghanistan and Iraq, stopping to shake hands with several Polish soldiers at the airport before he took off for Bucharest, Romania.
"As my mother would say -- and I don't know how this translates into Polish -- God love you," Biden said.
After he landed in the Romanian capital, Biden went to the residence of U.S. Ambassador Mark Gitenstein, where he planned to stay the night.