(CNN) -- Indiana's top two state lawmakers pledged Monday to amend the state's controversial "religious freedom" law to clarify that it cannot be used to discriminate against gay people.

Republicans David Long and Brian Bosma, the state legislature's senate president pro tempore and house speaker, respectively, insisted Monday that the law would not and was not intended to allow discrimination against anyone.

"It is not the intent of the law to discriminate against anyone and it will not be allowed to discriminate against anyone," Long said. "To the extent that we need to clarify through legislative action that this law does not and will not be allowed to discriminate against anyone, we plan to do just that."

The pair came out repeatedly hammering home that the law was not intended to and would not allow businesses to deny services to gay and lesbian individuals in Indiana, which Indiana's Republican Gov. Mike Pence repeatedly refused to say several times during an interview Sunday on ABC's "This Week."

The GOP leaders' press conference also came a day after Pence said that "we are not going to change this law," claiming that a legislative fix to the law was "not on my agenda."

It is clearly now on the Indiana Republicans' agenda, with the two top legislators explaining that their decision to fix the law came after even supporters of the law asked for the lawmakers to add language to clarify the law's intent.

A swift and heavy backlash emerged after Pence signed the bill into law last week, with businesses pledging and threatening to take their business away from the state. And Connecticut Gov. Dannel Malloy, a Democrat, announced Monday on Twitter he would make changes to policies on "state-funded travel," suggesting he might bar the use of state funds to travel to Indiana.

"When new laws turn back the clock on progress, we can't sit idly by. We are sending a message that discrimination won't be tolerated," he tweeted.

Bosma said legislators "didn't see that [reaction] coming" and said he and Long were already working with legislators in their respective chambers to "fix" the law.

"What we had hoped for with the bill was a message of inclusion -- inclusion of all religious beliefs," Bosma said. "What instead has come out is a message of exclusion and that was not the intent and hopefully not the effect. But to the extent that it is we are intent on righting that."

But Indiana's top GOP lawmakers also stuck to the line that the law, in its current form, could not be used to discriminate against LGBT individuals and that any other understanding was a result of "mischaracterization" and "misperception. They also insisted the law had been "misconstrued" and "misrepresented," wagging their fingers at the media and groups opposed to the Religious Freedom Restoration Act, dubbed RFRA.

The state's Democratic legislators said Monday Republicans' proposed "fix" would not be enough to blunt the damage the law has done to the state's image around the country.

"If Republicans want a fix, there's only one choice. And that is to repeal this law," Sen. Tim Lanane, the state senate's minority floor leader, said as he waived around papers he said would repeal the law and expand Indiana's civil rights act to protect "all Hoosiers."

"There is no compromise when it comes to discrimination. Let's start with a full repeal of RFRA. Repeal, repeal, repeal," he said.

House Democratic Leader Scott Pelatht said it was "time [Republicans] admitted that they made a horrible mistake" and said the state would need not "a Band-Aid" or "a rush job," but significant action to show the state does not condone discrimination.

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