Charles Dharapak, AP
Secretary of Veterans Affairs Eric Shinseki speaks at a meeting of the National Coalition for Homeless Veterans in Washington, Friday, May 30, 2014.

JUNEAU, Alaska — Alaska's two U.S. senators said the resignation of U.S. Veterans Affairs Secretary Eric Shinseki alone won't solve the problems within the beleaguered VA system.

Republican Sen. Lisa Murkowski and Democratic Sen. Mark Begich had each been reserving judgment on Shinseki and had not joined with others who had been calling for him to step down.

Shinseki's resignation comes amid allegations of delayed medical care at VA facilities nationwide.

Murkowski, in a statement Friday, said the structural problem with the VA "is far larger than one man, and if true reform is to be enacted and felt within the VA, Shinseki should be the first of many, many more to depart the agency."

But from the state's vantage point, Shinseki, during his tenure, had taken a "keen interest" in helping to make changes to Alaska's VA health care system, "advancing many positive improvements," she said.

Begich said Shinseki's resignation won't fix the reported problems.

Begich, who sits on the Senate Veterans Affairs Committee, said he would "aggressively" monitor the results of internal reports and demand answers so the VA nationally can achieve the kind of progress that he said has been made in Alaska. This progress includes partnerships with local clinics to ease patient backlogs and reduced wait times to see doctors, he said.

"The VA needs strong leaders now more than ever before," Begich said in a statement. "That's why I will push to swiftly find a new leader so we can get back to doing the important business of providing veterans the quality care they need and deserve."

Some of Begich's political opponents had seized on the VA's problems and suggested Begich hadn't been doing enough to address the matter. His campaign manager called politicizing the situation "disgraceful."

One of Begich's Republican rivals, Dan Sullivan, who had demanded Shinseki's resignation, called his ouster a "necessary first step." Sullivan said the Senate should act on legislation that would make it easier to fire or demote VA executives based on job performance.