The US, Britain, Norway and Canada say they are concerned by "credible reports" that Sudan's security forces have used live ammunition against demonstrators demanding that President Omar Bashir step down.
In a joint statement issued late on Monday in Khartoum, the four nations urged all parties to avoid violence or the destruction of property while affirming the right of the Sudanese people to peacefully protest to express their "legitimate grievances."
Amnesty International meanwhile said it had "credible reports" that Sudanese police have killed 37 protesters in clashes during the anti-government demonstrations that erupted last week across much of the country.
It said the use of lethal force by security forces against unarmed protesters was "extremely troubling" given that more protests were planned for Tuesday.
A coalition of independent professional unions has called for a march on the presidential palace in Khartoum to submit a petition demanding that President Omar Bashir, who rose to power in a 1989 military coup, step down. Two of Sudan's largest political parties called on their supporters to take part.
The protests began last Wednesday, initially over rising prices and shortages of food and fuel, but later escalated into calls for Bashir to go. The government has acknowledged fatalities during the protests but gave no figures. An opposition leader said over the weekend that 22 protesters were killed.
In a statement posted on the Facebook page of the US Embassy, the four nations called on the government to "respond to demonstrations appropriately, through uniformed police acting in accordance with Sudanese and international human rights law."
They called on authorities to "avoid the use of live fire on protesters, arbitrary detention, and censorship of the media," and to investigate alleged abuses.
The military vowed on Sunday to rally behind Bashir and emphasised in a statement that it was operating in harmony with the police and Sudan's feared security agencies.
Bashir on Monday said his government would introduce measures to remedy the economy and "provide citizens with a dignified life."
The demonstrations have been met with a heavy security crackdown, with authorities arresting more than a dozen opposition leaders, suspending school and university classes, and imposing emergency rule or night-time curfews in several cities. There has also been a near-total news blackout on the protests.
Bashir, in his mid-70s, seized power in a 1989 military coup that overthrew an elected but ineffective government. He is wanted by the International Criminal Court for committing crimes against humanity and genocide in the western Darfur region.
Australian Associated Press