The University of Houston has made a lot of progress in recent years. Lawmakers and school leaders say it's gained enough ground for the state to put it on the same playing field as its most elite schools: The University of Texas and Texas A&M.

Currently UT and A&M are the only universities in the state allowed to dip into the Permanent University Fund, a state-owned investment fund that funnels billions to the schools.

UH wants a piece of it.

It's a long shot -- it would require an amendment to the state Constitution, which means the bill would have to be approved by two-thirds of the members in both legislative chambers and a majority of voters -- but lawmakers considering a bill to open the fund up to UH said Wednesday that it's a conversation Texas needs to have as the state competes with the likes of California in elevating its national profile.

"This is to say to people in the state of Texas, 'We need to have this conversation,'" Rep. Sylvester Turner, a Houston Democrat who authored the bill, said. "I believe we should be viewed and seen and treated on the same level as the University of Texas System and the A&M System. I say put us in the game and treat us the same."

UH is Texas's best shot at elevating the state's profile beyond UT and A&M, officials argued Wednesday. It's the only university other than UT and A&M to earn a prestigious top-tier designation from the Carnegie Foundation for the Advancement of Teaching.

"I believe California has nine Tier 1 universities; Massachusetts has seven," Welcome Wilson, Jr., vice chair of the UH Board of Regents, told the committee. "We in Texas are far behind. We need to be looking at how to move multiple universities forward."

UT and A&M have an unfair advantage, UH advocates argued. Money from the Permanent University Fund helps UT and A&M receive millions more than any other school in the state. In 2014, the state sent $68.9 million to UH's main campus, compared to $296.4 million to UT Austin and $176.3 million to A&M's College Station flagship.

Turner's bill would essentially cut UT's chunk of the fund in half and give that half to UH. UT supporters told the committee that taking money from UT isn't the right way to help elevate other state universities.

State higher education funding has gradually decreased over the last several years. Texas now funds 13 percent of the University of Texas at Austin's budget, for example, compared with 47 percent 30 years ago. That means UT and A&M rely more than ever on the Permanent University Fund's consistent cash flow, UT supporters said.

"I want the University of Houston to be the best it can be. For them to continue to excel, we need to invest -- seriously invest," said Melinda Perrin, a UT alumnus and Houston resident who has served on various institutional governing boards. "What you have before you is a quick fix for one campus and one city at the detriment of 14 campuses across the state."

The bill was left pending, but committee members thanked Turner for filing it and starting the conversation.

"I think it is a discussion we need to be having," state Rep. Donna Howard, an Austin Democrat and the committee's vice chair, said.