"It's certainly in the interests of the United States for those parties to resolve their differences in a way that doesn't inject instability and volatility into the global financial market," Earnest told reporters.
US President Barack Obama's spokesman stressed the importance for Greece to build on structural economic reforms alongside returning to sustainable growth.
"Given that all of the parties acknowledge that these priorities are in their collective best interest, we're optimistic that they will be able to do that," he said.
Greece's national debt stands at around $350 billion, of which $270 billion is owed to its three biggest lenders, the International Monetary Fund (IMF), the European Union and the European Central Bank.
Greece was due to make a scheduled $330-million repayment to IMF on Friday, but decided to skip the deadline. Instead, it said it would bundle all of its current four IMF debt repayments in a single package before the June 30 deadline.
The move raised questions around Greece's ability to pay off its massive debt, prompting Earnest to emphasize on Sunday the importance of avoiding "brinksmanship" and sticking to deadlines.
