Khan, a former captain of Pakistan’s national cricket team, has denied the allegations and accused the ruling Pakistan Muslim League-Nawaz (PML-N) of organising a smear campaign in the run-up to elections next year.
Gulalai announced in Islamabad that “Imran Khan’s list of sins is very long” and that she decided to speak out because she does not want to compromise her integrity.
Gulalai has not released any of the alleged text messages.
Social media storm
Abbasi told the National Assembly on Friday that he wanted a special panel to investigate the allegations.
“We respect the person who has made the accusation, but we also respect the accused, and it is their right to be able to contest these allegations,” he said.
The accusations came just days after Pakistan’s Supreme Court disqualified the PML-N’s Nawaz Sharif, Khan’s long-time political rival, for lying on a wealth declaration.
Khan held a rally of his supporters last weekend in the capital, Islamabad, to celebrate Sharif’s removal as prime minister.
The scandal has stirred a social-media storm and prompted a debate on sexual harassment in Pakistan.
The backlash targeting Gulalai, in particular, has drawn criticism from women’s rights activists, who said the claims should be investigated rather than met with threats of violence.