President Bush said Sunday he appreciates the new British government's "strong response" to terrorist threats in London and Scotland that prompted the United States to tighten airport security and add air marshals to overseas flights. "It just goes to show the war against these extremists goes on," Bush said as he waited for Russian President Vladimir Putin to arrive at the Bush family seaside home at Kennebunkport, Maine. "You never know where they may try to strike, and I appreciate the very strong response that the Gordon Brown government's given to the attempts by these people." Bush remarked hours after his homeland security chief said the administration was satisfied with its current terrorism alert level following an attack at a Scottish airport and two foiled car bombs in London. "I think given what we know now, we're comfortable that we're at the right posture," Homeland Security chief Michael Chertoff said during a round of television talk show appearances. US airports and mass transit systems are tightening security ahead of the Fourth of July holiday and more air marshals will travel on overseas flights. "We will be doing operations at various rail locations and other mass transit locations in cooperation with local authorities. Again, not because of a specific piece of credible threat information, but because we are going into a holiday season. There will be a larger number of people traveling," Chertoff said. A US official, who spoke on condition of anonymity while the investigations were ongoing, said American authorities are running the names of the suspects in Britain through their databases to look for links to the United States. Those checks would include watch lists such as the no-fly list; any clue that the suspects had shared an address with people in the US; intelligence indicating the suspects made calls into the US; and other similar types of investigative work. It was not immediately clear if counterterrorism agencies had any hits or connections. Airports are at the second of five security threat levels - orange - indicating a high risk of terrorist attacks. The current national threat level is yellow, or the third highest, indicating an elevated threat. Chertoff said he does not plan to change those levels. "At this moment we don't have a specific credible threat against the United States," he said. Britain has raised its security alert level to the highest possible level, indicating terror attacks may be imminent. Chertoff said he has spoken out for some time about US worries involving potential terrorist threats originating in Britain and Europe. "I think one of the issues we're increasingly concerned about is the movement of Europeans, including people with European citizenship, into areas of South Asia to get trained and get experience and then the prospect of these people coming back to carry out operations in Europe or in the United States using Europe as a departure point," Chertoff said. "It's one of the reasons we've been very focused on increasing our security for people incoming from Europe. And that's something we're going to be looking at for the rest of the summer," he said. Chertoff said officials are also concerned about the possibility of a copycat attack in the US, saying it is "another reason why we have put some additional security measures in place." The US increased the number of air marshals on flights between the United States and Europe last August and stepped up the pace over the past few months, Chertoff said. Last August, British police foiled an alleged plot by Muslim extremists to use liquid explosives to blow up as many as 10 flights between the United States and Britain. "We haven't singled out Glasgow until a couple of days ago as a particular location for focus, but there has been a strategy of mixing up the deployment of these air marshals, sometimes more in one destination, sometimes more in another destination," he said. "Going forward, we will be doing some enhanced air marshal work and similar types of activities with respect to UK travel." Britain's new prime minister, Gordon Brown, said his country was dealing with terrorists associated with al-Qaida. Chertoff said, "If they are comfortable in confirming that, then that's fine. I have no reason to disagree." A burning Jeep Cherokee rammed into Glasgow's airport terminal on Saturday. The day before, police in London found two cars packed with explosives. One of the men in the airport attack was in critical condition at a hospital with severe burns, while the other was in police custody. Kenny MacAskill, the nation's justice secretary, said the two men were not born and raised in Scotland. "Any suggestion to be made that they are homegrown terrorists is not true," MacAskill said. Chertoff mentioned Iraq as a place where would-be terrorists can hone their skills in preparation for possible attacks around the world. "What I do think we see in Iraq is a laboratory for techniques where people experiment with sophisticated forms of explosive devices, and we do get concerned that that will ultimately lead to importing those kinds of techniques to the West." Chertoff appeared on NBC's "Meet the Press," ABC's "This Week," "Fox News Sunday" and "Late Edition" on CNN.