Evacuees escaping the floodwaters rest at the George R. Brown Convention Center that has been set up as a shelter in Houston. More than 9,000 people were staying at the center.

HOUSTON — With its flood defenses strained, the crippled city of Houston anxiously watched dams and levees Tuesday to see if they would hold until the rain stops, and meteorologists offered the first reason for hope — a forecast with less than an inch of rain and even a chance for sunshine.

The human toll continued to mount, both in deaths and in the ever-swelling number of scared people made homeless by the catastrophic storm that is now the heaviest tropical downpour in U.S. history.

The city’s largest shelter was overflowing when the mayor announced plans to create more space for thousands more people by opening two and possibly three more mega-shelters.

“We are not turning anyone away. But it does mean we need to expand our capabilities and our capacity,” Mayor Sylvester Turner said. “Relief is coming.”

Louisiana’s governor offered to take in Harvey victims from Texas, and televangelist Joel Osteen opened his Houston megachurch, a 16,000-seat former arena, after critics blasted him on social media for not acting to help families displaced by the storm.

Meteorologists said the sprawling city would soon have a chance to dry out.

When Harvey returns to land Wednesday, “it’s the end of the beginning,” National Hurricane Center meteorologist Dennis Feltgen said.

Harvey will spend much of Wednesday dropping rain on Louisiana before moving on to Arkansas, Tennessee and parts of Missouri, which could also see flooding.

But Feltgen cautioned: “We’re not done with this. There’s still an awful lot of real estate and a lot of people who are going to feel the impacts of the storm.”

The weather service forecast less of an inch for Houston on Wednesday, and only a 30 percent chance of showers and thunderstorms for Thursday. Friday’s forecast called for mostly sunny skies with a high near 94.

In all, more than 17,000 people have sought refuge in Texas shelters and that number seemed certain to increase, the American Red Cross said.

The city’s largest shelter, the George R. Brown Convention Center, held more than 9,000 people, almost twice the number officials originally planned to house there. The crowds included many from outside Houston.

Louisiana Gov. John Bel Edwards said he expected Texas officials to decide within 48 hours whether to accept his offer, which comes as Louisiana deals with its own flooding. About 500 people were evacuated from flooded neighborhoods in southwest Louisiana, Edwards said.

The city has asked the Federal Emergency Management Agency for more supplies, including cots and food, for an additional 10,000 people, said the mayor, who hoped to get them no later than Wednesday.

Almost four days after the storm ravaged the Texas coastline as a Category 4 hurricane, authorities had confirmed only six deaths — including a woman killed Monday when heavy rains dislodged a large oak tree onto her trailer home in the small town of Porter and another woman who apparently drowned after her vehicle was swept off a bridge.

Houston police confirmed that a 60-year-old officer drowned in his patrol car after he became trapped in high water while driving to work.

Six members of a family were feared dead after their van sank into Greens Bayou in East Houston. A Houston hotel said one of its employees disappeared while helping about 100 guests and workers evacuate the building.