President Bush and Russian President Putin Thursday demonstrated the close relationship the two have developed since first meeting last June while playing down their failure to reach an accord on a nuclear missile defense shield.

The two leaders spoke to reporters in Texas on the final day of a three-day summit.

Bush wants to develop a shield but must first withdraw or renegotiate the 1972 Anti-Ballistic Missile Treaty. Russia opposes any changes in the treaty, which Putin says is the foundation of the U.S.-Russian security framework.

"We have a difference of opinion. But the great thing about our relationship is our relationship is strong enough to endure this difference of opinion, and that's the positive development: that we found many areas in which we can cooperate and we've found some areas where we disagree, but, nevertheless, our disagreements will not divide us," Bush said during a question-and-answer session between the Russian and U.S. presidents and students at a high school in Crawford, Texas.

Putin added: "We differ in the ways and means we perceive that are suitable for reaching the same objective. And given the nature of the relationship between the United States and Russia, one can rest assured that whatever final solution is found, it will not threaten or put to threat the interests of both our countries and of the world."

In a separate event Thursday, National Security Adviser Condoleezza Rice said the parties made no progress on renegotiating the ABM Treaty and the United States will maintain the timeline to withdraw from the treaty in six months. In order to keep negotiations open, though, Rice said U.S. officials informed their Russian counterparts of the U.S. timeline for future testing.

Back at the high school, the presidents did agree on the need to combat terrorism around the world.

Bush said American military operations in Afghanistan will not stop until the members of the Al Qaeda terrorist network are brought to justice. He called the Taliban, "the most repressive, backward group of people we have seen on the face of the Earth in a long period of time... particularly in how they treat women," and said the U.S.-led coalition "will free the women of Afghanistan" while developing a stable government in Afghanistan that will not threaten the region.

The two leaders took almost a dozen questions from students, far more than they have allowed from journalists during the three-day summit that spanned Washington and Crawford. In a good-natured bit, Putin conditioned his responses, insisting that the students pose "only questions. No math questions, please."

Bush quickly agreed, "Good idea. Particularly, no fuzzy math questions," he said, referring back to a campaign debate with Al Gore about the surplus.

The two also ribbed one another like a long-playing comedy duo.

On a future meeting between the two, Bush said he told Putin the latter was welcome back to Crawford next August "for a true taste of Crawford."

Bush said Putin responded by telling Bush: "Fine, and maybe you'd like to go to Siberia in the winter."

On a more serious note, Bush responded to a question about nuclear warhead cuts by saying his commitment is to destroy, not merely disarm, the weapons.

On Tuesday, Bush announced that the United States would cut its missile stockpile by about two-thirds to 1,750-2,250 warheads. Bush said Thursday he thought Putin would make a similar declaration shortly and added that they now will focus on a related challenge.

"We're working on counterproliferation, which is an incredibly important issue, to make sure that arms and potential weapons of mass destruction do not end up in the hands of people who will be totally irresponsible, people that hate either one of our nations," Bush said.

The men also reiterated a statement from earlier this week that policy differences will not mean the two countries will return to an oppositional stance.

I believe the U.S.-Russian relationship is one of the most important relationships that our country can have," Bush said, adding, "It's one thing for he and me to have a personal relationship. The key is that we establish a relationship between our countries strong enough that it'll endure beyond our presidencies."

Putin said he was very surprised by his trip to Texas, a state that Russians are more familiar with than other parts of the country because of its close ties to Russia.

"Like in Russia, here in Texas the oil business is quite well developed, and we have numerous contacts in this area. And we have very many contacts in such areas as high tech and the exploration of space. And the fact that the parliament of the state of Texas declared April the 12th, the day when Yuri Gagarin, the first man to fly to space, accomplished this, as a state holiday, like it is a national holiday in Russia, is yet another testimony of the closeness of our outlook and achievements," Putin said.

Fox News' James Rosen contributed to this report.