More than 600,000 veterans will remain uninsured next year if there isn't movement to further expand Medicaid under Obamacare, according to a report from the left-leaning think tank Urban Institute.

The group's report said if the 19 states that haven't expanded Medicaid coverage hold to that position in 2017, it would leave 604,000 veterans without coverage.

The report also found that the uninsured rate for veterans and their family members sharply declined from 2013 to 2015. It fell from 11.9 percent in 2013 to 6.8 percent in 2015, a 42 percent drop.

"Over this time, veterans also experienced fewer unmet health needs, suggesting that increased coverage translated into improved access to care," according to the report funded by the Robert Wood Johnson Foundation. The decline mirrors a decline in the overall U.S. uninsured rate to below 9 percent.

However, coverage gaps remain for veterans, and the report said expansion of Medicaid could help.

Declines in veteran uninsurance rates were larger "in the 26 states that had expanded Medicaid under the [Affordable Care Act] by 2014 than in non-expansion states," the report said.

A 2012 Supreme Court decision left it up to states to decide whether to expand Medicaid. So far, 31 states have done so and 19 have held out. Most of those 19 states are led by Republican governors.

The federal government covers the entire cost of the expansion for the first few years, but then asks for states to shoulder some of the cost. States that have held out have done so due to concerns about long-term costs and opposition to Obamacare.

The report said the Department of Veterans Affairs agency is able to provide care to veterans in some cases.

"Although we do not attempt to assess eligibility for VA care, many low-income veterans likely would be eligible to obtain care through the VA's healthcare system," the report noted.

The VA provides care to veterans but only certain veterans meet eligibility requirements, which include a minimum duty requirement. There is also enhanced eligibility status for former veterans of wars such as Vietnam and the first Gulf War.

The report's results on the uninsured rate for veterans was based on a survey of 4,000 non-elderly veterans.