At his first stop, in London, he drew criticism from British political leaders when he appeared to question whether the nation was fully prepared for the Olympic Games, now underway.
The Republican presidential contender has been highly critical of China throughout his campaign, promising to challenge Beijing's growing influence in East Asia and get tougher with the communist government on its human rights record.
There was some tension between reporters and Romney aides as the campaign looked to Poland as a final opportunity to project the image of a leader ready to stand on the world's stage.
The two-day trip to Poland was aimed in part at building support among Polish-American and Catholic voters in the United States.
Poles generally have been skeptical of Obama's "reset" with Russia, and Romney has cited Polish concerns in his criticism of Obama. Some in Poland and the neighboring Czech Republic were upset by the Obama administration's decision to revise the Bush-era missile defense plan for Europe, which included sites in both countries.
In his speech, Romney said of Poland: "At every turn in our history, through wars and crises, through every change in the geopolitical map, we have met as friends and allies. That was true in America's Revolutionary War. It was true in the dark days of World War II. And it has been true in Iraq and Afghanistan."
Romney delivered his remarks in a deeply Roman Catholic country that for years has favored Republicans over Democrats. This is partly a legacy of President Ronald Reagan, whose efforts helped bring down communism across Eastern Europe, for which Poles remain grateful.
Poland has been a stalwart U.S. ally and significant contributor to military operations in Iraq and Afghanistan.
Romney met earlier in the day with Polish Foreign Minister Radoslaw Sikorski. They discussed the longstanding ties between the two nations as well as the conflict in Afghanistan.
"On behalf of our countrymen, I express deep appreciation for your willingness to fight with us, to stand with us, and to be our friends in times of crisis and military conflict," Romney said.
"Poland has excellent ties with the United States, regardless of which American party is in power," Sikorski said. "We remember Ronald Reagan's warm feelings for Poland's Solidarity and also the fact that we joined (NATO) during Bill Clinton's term."
Romney also stopped to view a memorial to Pope John Paul II, who was born in Poland. He then met with President Bronislaw Komorowski.
The candidate ignored shouted questions from reporters about his comments on Israel and the Palestinians. Asked why Romney has taken just three questions from American reporters during the trip, traveling press secretary Rick Gorka said, "Shove it." He later called some journalists to apologize.
Romney's visit, campaign officials said, was at the invitation of Lech Walesa, the Polish labor leader who co-founded the Solidarity movement and served as the country's president during the country's transition out of communism.
Walesa effectively endorsed Romney when they met Monday.
But Solidarity, the organization Walesa helped found more than two decades ago, characterized Romney as being hostile to unions and against labor rights. It emphasized that it had no role in organizing the visit and expressed support for American labor organizations.
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