(CNN) -- Hours before being honored for his peacemaking efforts, Tony Blair revealed a secret weapon: Bill Clinton.
The former U.S. president was constantly on the phone with Blair during the Northern Ireland peace process in 1998, providing analysis and advice that proved crucial to reaching an agreement, the former British prime minister said Monday.
"He played an absolutely critical role," Blair said of Clinton on Monday as the two sat side-by-side to answer questions before the evening ceremony where Blair was to receive the 2010 Liberty Medal from the National Constitution Center in Philadelphia, Pennsylvania.
"Without your intervention, we would never have achieved that peace in Northern Ireland," Blair said to Clinton, adding that he never had the chance to publicly thank him.
The hour-long session featured anecdotes and rare insight on historical developments of the 1990s, when Clinton was U.S. president and Blair became the British prime minister.
The Liberty Medal, an annual award given by the nonprofit constitution center that has Clinton as its board chairman, went to Blair this year for "his steadfast commitment to conflict resolution," the group's website says.
Along with the Northern Ireland peace agreement he helped mediate, Blair was cited for his role in Middle East peace negotiations and the work of his Tony Blair Faith Foundation in promoting global understanding.
Asked about the necessary components for successful peace talks, Blair joked that "blind luck" was essential. He then listed the willingness of the participants, a framework agreement on basic principles and perseverance as the key factors.
"Never give up. No matter how difficult it is, no matter how hard it is, just keep going," Blair said as Clinton nodded in agreement.
In the Northern Ireland talks, Blair said, the acute focus on the negotiations created an expectation that helped force participants to reach an agreement.
"It was, in a sense, luck that we got into such a hothouse atmosphere that people began to feel it was more embarrassing not to do the deal than to do it," Blair said.
Clinton added that it was important for outside parties to help warring nations or factions realize the benefits and future possibilities of peace.
"We've got to paint a picture of what this is like at the end of the road, and we have to be there to help maximize the benefits and minimize the risks," Clinton said.
On several occasions, Blair mentioned particular advice or help he received from Clinton, such as strong U.S. support for European intervention in the Kosovo conflict to stop forced removals and killings of Muslims by Serb forces.
"The truth is, without America and without President Clinton coming in, we couldn't have handled that," Blair said.
Such backing reflected the longstanding "special" relationship between their countries, and Blair insisted that the shifting global dynamics of the 21st century made that partnership more vital than ever.
He called the relationship "something living and breathing now, with relevance today and tomorrow, and we should keep it."
To Clinton, the shifting role of the two industrial powers made their relationship important for everyone.
"On balance, it's been a good thing for the world because we're not imperialists anymore and whatever we do, we do partly because we have a capacity most other countries don't," he said.
Both men listed the economic rise of China as a major current issue, and Blair also mentioned the growing role of religious extremism.
"It's there, and it's powerful and it's not, I'm afraid, going away," he said.
For his part, Clinton said, a changing dynamic in the Arab world made a Middle East peace agreement more possible now than 10 years ago, when he was president.
Back then, he said, Arab leaders privately encouraged him to seek an Israeli-Palestinian peace agreement but were unable to publicly endorse a proposed deal for political reasons.
Now, he said, the Arab world fears the rise of Iran as a regional power and threat, and therefore seeks a sustainable relationship with the United States and Israel.
"The most hopeful thing is that the Arabs want this done," Clinton said of renewed peace talks guided by his wife, Secretary of State Hillary Clinton.