(CNN) The White House asked Sen. Kevin Cramer to block a motion calling the mass killing of Armenians by the Ottoman Empire a "genocide" and the North Dakota Republican complied, Cramer told CNN on Thursday.

The White House approached Cramer's foreign affairs team in search of a senator to stop a unanimous consent request -- which allows legislation with wide support to pass without holding a roll call vote, as long as no senator objects -- on an Armenian genocide resolution. Cramer said the White House wanted the resolution blocked because President Donald Trump had just met with the Turkish President at the NATO summit.

CNN has left a message with the White House seeking comment on Cramer's claim.

Cramer's objection on Thursday sank the bipartisan measure. The move comes following the House's approval of a resolution in October acknowledging "the killing of 1.5 million Armenians by the Ottoman Empire from 1915 to 1923."

The resolution aims to send a strong message to the Turkish government amid deteriorating relations between American lawmakers and Turkey. The designation as a genocide would mark a significant political development, as Turkey maintains to this day the killings did not constitute a genocide and disputes the death toll, putting the figure closer to 300,000.

Cramer said he agreed with the White House's reasoning but doesn't plan to object again, predicting that the resolution will ultimately pass.

"I don't know that it can be objected to much longer," he told CNN.

Axios first reported on the request from the White House.

Democratic Sen. Bob Menendez of New Jersey and Republican Sen. Ted Cruz of Texas co-sponsored the unanimous consent request.

Cruz told reporters Thursday after Senate votes that it was "a mistake for us to refuse to acknowledge this."

He and Menendez have tried repeatedly to pass the resolution but "have faced a series of objections" that are being "raised on behalf of the administration," the Texas Republican said.

The White House has been very candid about blocking the bill because it's in the process of negotiating with Turkey on a number of issues and "they don't want to irritate the Turks," he said.

"Turkey is a NATO ally and they're an important NATO ally, but that doesn't mean we have to ignore the truth and ignore reality," Cruz said. "Twelve other NATO allies have acknowledged the Armenian genocide -- they continue to work with Turkey."

But Cruz said he's hopeful they'll eventually get it passed to finally acknowledge the "horrific atrocity" that was the Armenian genocide.

Cramer predicted that "if Senator Menendez (proposed the resolution) every week, the day of passing it won't be long."

"I don't know what the right time is, but this isn't it," Cramer continued. "And maybe there's never a perfect time. But at some point, he'll succeed, it's my belief."