The US envoy to Sudan has expressed Washington's support for the protest movement and called for a civilian-led government.
Donald Booth on Wednesday urged the military to stop attacking protesters.
The army took control of the country in April, after removing longtime autocrat Omar Al Bashir following months of mass protests against his rule.
But when the protests continued, the ruling generals cracked down heavily to disperse the crowds.
Mr Booth urged an independent investigation into the crackdown in which more than 100 died.
Tension between the generals and leaders from the umbrella protest movement, the Alliance for Freedom and Change, remain high.
Rallies on June 30 were called by the alliance to coincide with the 30th anniversary of the coup that had brought Mr Al Bashir to power.
But veteran opposition leader Sadiq Al Mahdi rejected the call for nationwide strikes on Wednesday.
"Our opinion is to avoid escalatory measures from either side," Mr Al Mahdi said at his party headquarters in Omdurman, the twin city of Khartoum across the Nile.
Mr Al Mahdi said any escalation before receiving the ruling military council's response to a power transfer plan proposed by Ethiopia would be premature.
Ethiopia is mediating talks between the generals and protest leaders since negotiations collapsed after the June 3 crackdown.
Sudan's ruling generals and an opposition coalition have been wrangling for weeks over what form a transitional government should take.
Ethiopia's proposal calls for forming a 15-member civilian-majority governing body, which the protest leaders have accepted but the military council has so far dismissed.
On Tuesday, a US State Department official who deals with Sudan said that Washington was considering all options, including sanctions, if there were more violence.
Makila James, deputy assistant secretary for East Africa and the Sudans, said they could include visa sanctions or economic sanctions.
"We want to use the right tool and we want to target the right people," Ms James said.
The US previously sanctioned Sudan under Mr Al Bashir over its support for militant groups and the civil war in Darfur.
Saudi Arabia and the UAE have offered a total of US$3 billion in aid to Sudan.