Franks declined to name who was floated as a potential standard-bearer for a third-party conservative bid.
A second attendee, requesting anonymity, said Senator Ben Sasse of Nebraska was mentioned as a possible late-entry contender who conservatives could rally around.
A spokesman for Sasse said he did not send a representative to the meeting.
Three people said the mood of the room was muted and downbeat. Attendees voiced frustration with the lack of co-ordination so far and wondered aloud whether Trump could be halted. The third-party scenario drew intense interest, but it also acknowledged it would be logistically and financially difficult with few major politicians willing for now to agree to take the political risk that such a run would entail.
Instead, a consensus emerged by the end that the best option may be working in upcoming primaries to boost Cruz and hope to prevent Trump from securing a majority of delegates and making a convention standoff the culmination of those efforts, the people said.
Senator Lindsey Graham said he's all in for Cruz in the Republican presidential primary, even if he's not so happy about it.
Graham, of South Carolina, called Cruz the best choice for Republicans who want to avoid nominating Trump in July.
"I prefer John Kasich," Graham said. "But I don't see how John Kasich can mount the opposition that Ted Cruz can to stop Donald Trump from getting 1237 [the number of delegates needed to secure the nomination]."
Graham, who withdrew from the presidential primary in December, has been consistently critical of Cruz and made it clear in January he wasn't thrilled about the idea of having to choose between Cruz and Trump.
Cruz yesterday named his national security advisers, including former staffers of President Ronald Reagan and members of a think-tank that has been called an anti-Muslim "hate group" by a civil rights organisation.
Among the most recognisable names on the US senator's list of 23 advisers was Elliott Abrams, who served in the Administrations of both Reagan and George W. Bush and is a senior fellow at the Council on Foreign Relations.
But the list of advisers drew more attention for its inclusion of several critics of Muslims. Among those were Frank Gaffney, a former official in the Reagan Administration, and at least two other members of a think-tank Gaffney founded, the Centre for Security Policy.
The centre's reports argue that hundreds of thousands of American Muslims support Islamist violence in the US and that there is a conspiracy to erode the US legal system by elevating sharia, the Islamic legal code.
The Southern Poverty Law Centre, a civil rights organisation that monitors US extremist groups, has labelled the Centre for Security Policy a "hate group" and Gaffney a "notorious Islamophobe".
A Gaffney spokesman pointed to online essays where Gaffney has rejected such criticism, saying his group is a defender of civil liberties against "Islamic supremacists".
The Council on American-Islamic Relations, a Muslim rights group, urged Cruz to reconsider having Gaffney and others who have made anti-Muslim remarks as his advisers, saying it suggested the candidate entertained "anti-Muslim bigotry".
Some of Cruz's other advisers have been critical of anti-Islamic rhetoric, including Abrams and Mary Habeck, another former Bush adviser; both have said Islam should not be demonised.
Another adviser is Katherine Gorka, president of the Council on Global Security, a group that produces research on Islamist violence.
On the Democratic side of the race, presidential candidate Bernie Sanders, responding to reports President Barack Obama had called on Democrats to rally around Hillary Clinton as the likely nominee, says it's "absurd" to suggest he drop out of the race when only half of voters have participated in the process.
- Bloomberg, AAP
