Updated

Texas residents braced for heavy rain and more flooding as the remnants of Tropical Storm Bill crept further inland Wednesday.

The center of the storm was expected to move northward, west of the Interstate 35 corridor. Forecasters called for 4 to 5 inches of rain in parts of central Texas that are still recovering from disastrous Memorial Day weekend floods that left 14 dead and two missing along the Blanco River.

The National Hurricane Center said early Wednesday the storm was about 40 miles east of Austin and moving north at about 13 mph. Flash flood watches and warnings were in effect for the area, and Gov. Greg Abbot was expected to receive a briefing from state emergency officials in the morning.

In North Texas, Dallas authorities were monitoring road conditions and Arlington residents were picking up sandbags being offered for free by city officials.

The National Weather Service predicts average rainfall of 3 to 6 for portions of Texas through noon Wednesday, though isolated areas could see up to 12 inches. Arkansas and Oklahoma could get up to 9 inches of rain in the coming days, and Missouri could get more than 7. The incoming weather is expected to complicate ongoing flood-containment efforts even more.

"We're more vulnerable to flooding right now than usual because we just got through the wettest month on record," Texas state climatologist John Nielsen-Gammon said.

The Memorial Day weekend storms brought widespread flooding to Oklahoma and Texas, killing more than 30 people overall. At one point last month, 11 inches of rain fell in some parts of the Houston area, resulting in flooding that damaged thousands of homes and other structures and forced motorists to abandon at least 2,500 vehicles across Houston.

Rafael Lemaitre, spokesman for the Federal Emergency Management Agency, said FEMA has paid nearly $38 million this year in Texas flood insurance claims, with the vast majority associated with last month's deluge.

FEMA personnel in Texas and Oklahoma are going to remain in the region and help clean up the aftermath from the tropical storm, White House spokesman Josh Earnest said Tuesday.

Major flooding could occur along the Trinity River as it extends through East Texas, according to the weather service, with one portion northeast of Houston nearly 4 feet above flood stage Tuesday. The Guadalupe River north of Corpus Christi also was swollen as it ran more than 5 feet above flood stage.

Twisters were also a possibility Wednesday, with 21 counties in the eastern half of the state under a tornado watch until 7 a.m.

The Associated Press contributed to this report.