"I didn't really take it as going after me," Ryan said in an interview with CNBC.
President Donald Trump tweeted that he told the two congressional leaders to link the debt ceiling increase -- which faces a deadline at the end of September -- to a Veterans Affairs bill that recently passed with wide support.
"They didn't do it so now we have a big deal with Dems holding them up (as usual) on Debt Ceiling approval. Could have been so easy-now a mess!" Trump tweeted
Ryan confirmed that tying the two bills together was "an option" that they were considering.
"But the VA deadline came up and we weren't able to do that then," he said.
A Senate GOP leadership aide told CNN earlier Thursday that members of the conservative House Freedom Caucus rejected the idea because they didn't want to have to vote against the popular veterans affairs bill. Members of the caucus and other "debt ceiling purists" won't support an increase unless it includes other provisions to curb government debt, like spending cuts. They "hated" the idea, the aide said.
Still, Ryan has maintained that he's not concerned about the debt ceiling, a must-pass move in order for the government to avoid defaulting on loans. Earlier, after taking a tour of Boeing in Washington state, Ryan told a group of employees in a question-and-answer session that Congress will pass a bill before the country hits the debt ceiling.
"There are many different options in front of us on how to achieve that," he said. "We'll do that because this is about paying the bills we already racked up, making sure we pay our debts. We pay our debts in this country, we will continue to do so. So I'm not worried that that's not going to get done, because that's going to get done."
Congress will face a busy month in September when it comes back from recess. Along with the debt ceiling, lawmakers must pass a budget or short-term resolution and find a solution to fund the State Children's Health Insurance Program by September 30. Also big on the legislative docket this fall is tax reform.