Egyptian President Abdul Fattah al-Sisi is visiting the White House for the first time since he led the military's overthrow of his predecessor in 2013.
US President Donald Trump said he was "very much behind" Mr Sisi, whose deadly crackdown on dissent was criticised by the Obama administration.
Mr Sisi declared his deep appreciation for Mr Trump's "unique" personality.
US officials have said Mr Trump is seeking to "reboot" the countries' bilateral relationship at the talks.
He also wants to "build on the strong connection" established with Mr Sisi when they met in New York in September, during the US election campaign.
As Egypt's defence minister and armed forces chief in July 2013, Mr Sisi led the overthrow of the country's first freely elected president, Mohammed Morsi, after mass protests against his rule.
The following month, he oversaw the violent dispersal of protests by supporters of Mr Morsi and his Muslim Brotherhood, which left more than 1,000 people dead.
Human Rights Watch says tens of thousands people have been arrested in a crackdown on dissent, and that security forces have committed flagrant abuses, including torture, enforced disappearances and likely extrajudicial executions.
Mr Sisi, who was elected president in May 2014, has also presided over severe restrictions on civil and political rights that have effectively erased the gains of the 2011 uprising that ousted Hosni Mubarak, according to the US-based group.
Barack Obama froze some US military assistance to Egypt in response to the crackdown in October 2013.
He insisted the restrictions would continue until Egypt showed "credible progress" towards democracy, but ended up restoring the military support in April 2015 because it was "in the interest of US national security".
A senior Trump administration official briefed reporters that human rights concerns would be raised at Monday's meeting, but that it would be handled in a "private, more discreet way."
"We believe it's the most effective way to advance those issues to a favourable outcome," the official added.
HRW's Washington director, Sarah Margon, criticised that approach.
"Inviting Sisi for an official visit to Washington as tens of thousands of Egyptians rot in jail and when torture is again the order of the day is a strange way to build a stable strategic relationship," she said.
The two presidents are also expected to discuss a range of regional issues, including efforts to revive the Israeli-Palestinian peace process and the battle against so-called Islamic State.
Since 2013, hundreds of Egyptian security personnel have been killed in attacks by an affiliate of the jihadist group that is based in the Sinai Peninsula.
To assist it in the fight against IS, Mr Sisi is believed to want an increase in the $1.3bn (£1bn) in military aid that Egypt receives annually.
The White House has promised to maintain a "strong and sufficient" level of support, but recently proposed drastic cuts to its international aid budget.
The administration official said Mr Trump was also "interested in hearing President Sisi's views on the Muslim Brotherhood", which the Egyptian leader wants the White House to designate a terrorist organisation.
Brotherhood officials insist that the group opposes violence. However, members of some of its regional offshoots have condoned or committed violent acts.