Mr. Giuliani in June and August met with top Ukrainian officials about the prospect of an investigation, he said in an interview. The Trump lawyer has suggested Mr. Biden as vice president worked to shield from investigation a Ukrainian gas company with ties to his son, Hunter Biden. A Ukrainian official earlier this year said he had no evidence of wrongdoing by Mr. Biden or his son.

After the July call between the two presidents, the Ukrainian government said Mr. Trump had congratulated the new president on his election and expressed hope that his government would push ahead with investigations and corruption probes that had stymied relations between the two countries.