Sen. John McCain, R-Ariz., said New York City Mayor Michael Bloomberg appears more focused on enhancing background checks on guns than on an assault weapons ban, as the mayor continues his push for tougher gun laws on Capitol Hill.

After the two met Wednesday to talk about gun violence measures, McCain said Bloomberg is also bullish on his chances to affect more congressional races around the country where gun control is an issue.

McCain said the mayor referenced Tuesday’s Democratic primary win of Robin Kelly to replace Rep. Jesse Jackson, Jr., D-Ill., and said he would continue to be active in congressional races. Bloomberg’s super PAC spent $2 million in about a month to defeat National Rifle Association-backed candidate Debbie Halverson.

McCain didn’t mention any specific races where Bloomberg may get involved.

The Arizona Senator said he and Bloomberg, with whom he has a friendly relationship, have known each other for many years and Bloomberg “visits me almost every time” he is in Washington.

“We talk about many issues; we disagree on some,” McCain said.

“But [this time] he specifically wanted to talk about the gun issue,” he continued. The two talked about Bloomberg’s legislative agenda, and McCain said an assault weapons ban may not be Bloomberg’s top priority.

In their talks, McCain said that the mayor “agreed that most of the murders and suicides are not with assault weapons. I think his biggest agenda is background checks, the gun show loop, more than the assault weapons ban, that is the impression I got.”

He said that he recommended Bloomberg speak with Sen. Tom Coburn, R-Okla., who is spearheading negotiations on background check legislation along with Sens. Joe Manchin III, D-W.Va., Charles E. Schumer, D-N.Y., and Mark S. Kirk, R-Ill. The quartet may offer their bill at a Senate Judiciary Committee markup on gun bills Thursday.

McCain said Bloomberg intended to try to seek Coburn out.

“I told him he should be encouraged that conversations are going on with Manchin, and Manchin talks to me quite frequently about what they are doing,” McCain said.

McCain noted that he and Bloomberg also spoke about the need for tax reform and “a whole bunch of stuff that we always talk about.”