By early Monday, tropical storm warnings for the southern tip of Baja California were discontinued but remained in effect farther north on the peninsula's west coast from Punta Abreojos to Santa Fe and along the east coast from La Paz to Mulege.
The storm had maximum sustained winds near 40 mph (65 kph). But forecasters expected the storm to weaken and become a tropical depression later in the day.
The U.S. Hurricane Center in Miami said Julio could dump 3 to 6 inches (7.5 to 15 centimeters) of rain on the normally parched Mexican peninsula, raising fears of flash flooding.
Most vacationers rode out the bad weather Sunday inside their hotel rooms, but some ventured out on shopping trips and excursions.
"They're very calm," said Jorge Castro, front desk manager at the hillside Hotel Finiterra. The 224 guests were warned to stay away from the ocean, but none made plans to leave early.
"They can see it's not a huge problem. Some have even gone out on activities, on tours, or sand biking," Castro added.
The storm was centered about 30 miles (45 kilometers) west-southwest of Loreto early Monday and was moving north-northwest near 15 mph (24 kph). Tropical storm force winds extended up to 70 miles (110 kilometers) from the storm's center.
The hurricane center said the storm should enter the northern Gulf of California by Tuesday.