The outcome of trade talks between the United States and China this week will play a major role in determining whether oil prices can continue to rally, analysts tell CNBC.

Oil prices have risen for six straight sessions, clawing back gains after falling to 1½-year lows last month. The cost of crude collapsed more than 40 percent between early October and late December on concerns about slowing economic growth and oversupply in the oil market.

Amrita Sen, chief oil analyst at research firm Energy Aspects, thinks crude futures have more room to run, but says the recovery is on shaky ground.

"I think as long as the global economy isn't collapsing, we should be able to climb a little bit higher, but it is going to be very fragile because the biggest, biggest uncertainty right now is the trade war going on between the U.S. and China," she told CNBC Europe's "Squawk Box" on Monday.

U.S. and Chinese trade representatives are meeting Monday and Tuesday to negotiate a path forward in the nations' ongoing trade dispute. The two countries have slapped tariffs on hundreds of billions of dollars worth of one another's goods.

Additional tariffs threaten to weigh on global economic growth, and consequently, demand for oil and fuel. This comes at a time when forecasters have already warned that oil demand will grow more slowly than previously anticipated in 2019.