The US has told Zimbabwe that there is an "urgent need to hold security forces accountable for acts of violence" earlier this year and last year.
Six people were shot dead in August 2018 as opposition protesters complaining about the election result clashed with security forces.
At the beginning of this year local rights groups said at least 12 people had been killed and many more beaten during demonstrations triggered by a hike in fuel prices.
At the time a government spokesperson said this was "a foretaste of things to come".
The US' top diplomat in Africa, Tibor Nagy, has tweeted that he brought the incidents up with President Emmerson Mnangagwa.
The US assistant secretary for African affairs met the president on the sidelines of a US-Africa meeting in Mozambique, AFP news agency reports.
He said the US wanted to see "real political and economic reforms".
When Mr Mnangagwa came to power in November 2017, after the ouster of long-time President Robert Mugabe, there were high hopes that he would make big changes.
Some have criticised the president for not moving fast enough.