PHOENIX — Sen. John McCain returned to Afghanistan to celebrate the Fourth of July with U.S. troops as a new round of terror bombings shook Saudi Arabia on Monday.

McCain, R-Ariz., the Senate Armed Services Committee chairman, told The Arizona Republic Monday that he hopes President Obama's administration won't repeat what McCain persistently has criticized as a major mistake of Iraq and withdraw U.S. forces prematurely.

The Taliban continues to control significance parts of the country, getting assistance from Pakistan's insurgent Haqqani network, he said.

The Haqqani network has crossed the border from North Waziristan, Pakistan, to carry out attacks against the U.S.-backed Afghan government.

"I'm very concerned about the proposed cutbacks in the troop strength in Afghanistan," McCain said by telephone as he was getting ready to return to Washington, D.C., for Senate business on Tuesday. "I think it will lead to the same result as it did when Obama pulled everybody out of Iraq. It's a matter of great concern. ... Right now, their plans are — unless they change, and I hope they will change — to go from 9,800 down to 5,500. That's not enough to defend the country against the Taliban."

McCain maintains that the security vacuum that occurred after the Iraq War officially ended in December 2011 directly led to the rise of the Islamic State, also known as ISIS or ISIL, in Iraq and Syria. The organization has claimed responsibility for recent deadly attacks in Baghdad and in Dhaka, Bangladesh. It also is suspected in an attack on Istanbul Ataturk Airport and in a wave of bombings Monday in three Saudi Arabian cities.

"It's the spread of ISIS," McCain said. "And it's a direct result of a lack of strategy and a failure on the part of the president of the United States."

The bipartisan Senate Armed Services delegation also included Sens. Joe Donnelly, D-Ind.; Lindsey Graham, R-S.C.; and Ben Sasse, R-Neb. Before Afghanistan, the group visited Pakistan, where McCain said he met with leaders to request their help in eliminating the Haqqani network, an organization that has some degree of support from inside the Pakistani government and "which obviously rotates into Afghanistan and has committed numerous acts of terror."

"We want their help," McCain said of Pakistani leadership. "We want a good relationship."

Back home, news of McCain's presence in Pakistan prompted one of his opponents in Arizona's Aug. 30 Republican primary to take a shot at him in a written statement.

“While most American families are spending their July 4th holiday weekend reflecting on the principles that have sustained this nation since the Declaration of Independence, Arizona’s senior senator is palling around in Islamabad," said Kelli Ward, a former state senator from Lake Havasu City and one of three Republicans challenging McCain for this year's Senate nomination.

Ward ripped McCain's “Invade the World, Invite the World” agenda, which she said includes "open borders and amnesty" in addition to questionable national-security priorities.

“The burden is on Senator McCain to explain what he is doing over there, who is he meeting with, what he is giving them, and why," Ward added.

While not directly responding to Ward's criticism, McCain emphasized the high stakes of the U.S. relationship with Pakistan.

"If this kind of (Haqqani network) activity continues, it can put the lives of American service members in danger," McCain said. "Pakistan has a sizable inventory of nuclear weapons. This is serious business here. I'll do whatever I can do to protect the men and women who are serving, but also to not have a crisis erupt that could mean this inventory of nuclear weapons they have could fall into the wrong hands."

Since the Sept. 11, 2001, terrorist attacks on New York City and Washington McCain has made it a point to try to spend the Fourth of July holiday with military stationed overseas.

"I have been going to Afghanistan for many, many years for the Fourth of July," McCain said. "It's a matter of record. I am proud to go. I am proud to spend time on our Independence Day with the men and women who are serving in our military. We awarded medals, we did re-enlistments, we had meals with them."

Follow Dan Nowicki on Twitter: @dannowicki