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6/12/2014 8:55 P.M. ET

Cousino among 28 Draft picks signed by Mariners

SEATTLE -- The Mariners have signed 28 of their 40 picks from last week's First-Year Player Draft, the club announced Thursday, including 13 of the first 14 selections.

The lone absentee in that top group now is first-rounder Alex Jackson, the 18-year-old catcher/outfielder from San Diego who was selected with the No. 6 overall pick. As of Thursday afternoon, only 11 of the 34 first-round selections in the Draft had signed.

Mariners second-rounder Gareth Morgan's signing was announced Tuesday, and the club finalized a deal Thursday with third-rounder Austin Cousino, a center fielder from the University of Kentucky.

Jim Callis of MLB.com reported Cousino agreed to a $400,000 bonus, which is below the allotted $693,200 for the No. 80 overall pick.

Paxton to begin increasing throwing program

SEATTLE -- Injured Mariners left-hander James Paxton will throw again on flat ground Saturday as he continues returning from back and shoulder issues that have sidelined him since his second start of the season on April 8.

Paxton threw at a 60-foot distance for seven minutes on Thursday and will increase that to a 10-minute session Saturday. The throwing program then will begin increasing in distance before he gets back up on a mound as he rebuilds his arm strength.

"He's improving every day," said manager Lloyd McClendon. "The doctors are pleased with where he is. I'm not sure when he'll throw off the mound, but he's getting close."

Paxton, who is 5-0 with a 1.75 ERA in six Major League starts, said trainers are telling him not to rush things after he had to shut down following a Minor League rehab start for Triple-A Tacoma in late May when his shoulder tightened up. He initially was sidelined with a strained lat muscle, and he said both issues are being monitored now.

"Everything at the moment is feeling really well, so we'll just take it day by day," said Paxton, who has thrown twice now since being shut down.

Taijuan Walker, the Mariners' other young hurler working back from injury, is scheduled to start Saturday for Tacoma at Nashville.

Worth noting

• Mariners catcher Mike Zunino ranked second among American League catchers with 18 extra-base hits going into Thursday's game, and was tied for the lead in home runs with Cleveland's Jan Gomes with seven.

• Zunino made his MLB debut one year ago on Thursday at age 22, becoming the first position player from the 2012 Draft to appear in the Majors. In his first calendar year, Zunino hit .218 with 12 home runs and 36 RBIs in 104 games and has quickly established himself as one of the top young defensive catchers in the AL.

• Boys and girls from around the Pacific Northwest will compete for the chance to go to the National Finals in Minneapolis at the Major League Baseball Pitch, Hit & Run Team Championship Competition at Safeco Field on Sunday following the Mariners-Rangers game.

The 24 competitors qualified for Sunday's Team Championship by placing first in their age divisions at their local competitions and becoming the All-Around Champions at their sectional competitions, which were held during May and June. Only the top three performers in each age group from the sectional competitions in the greater Pacific Northwest qualified for the Mariners Team Championship Competition.

Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.