The Transportation Department said late yesterday the civil penalties will settle investigations into how Toyota dealt with recalls over accelerator pedals that could get trapped in floor mats, and steering relay rods that could break and lead to drivers losing control.

The latest settlement, on top of a $16.4 million fine Toyota paid earlier in a related investigation, brings the total penalties levied on the company to $48.8 million. It caps a difficult year for the world’s No. 1 automaker, which recalled more than 11 million vehicles globally since the fall of 2009 as it scrambled to protect its reputation for safety and reliability.

Toyota’s board of directors agreed to pay the fines today at the company’s board meeting in Japan, according to an official familiar with the case, and the company said it agreed to the penalties without admitting to any violations of US laws. However, that does not free Toyota from potential civil and criminal penalties in private lawsuits and other federal investigations.

The person had spoken earlier yesterday on condition of anonymity ahead of the formal announcement.

Steve St. Angelo, Toyota’s chief quality officer for North America, said in a statement that the company has “worked very hard over the past year to put these issues behind us and set a new standard of responsiveness to our customers. These agreements are an opportunity to turn the page to an even more constructive relationship with NHTSA (National Highway Traffic Safety Administration).’’

In April, Toyota agreed to pay the maximum fine allowed under law for a single case — $16.4 million — for failing to promptly alert US regulators to safety problems over sticking accelerator pedals. Under federal law, automakers must notify NHTSA within five days of determining that a safety defect exists and promptly conduct a recall.

At the time, Toyota denied attempting to hide a safety defect and said it agreed to the penalty to avoid a lengthy legal battle with the government.

The latest fines involve two separate safety problems affecting certain Toyota passenger cars and trucks.

The first case deals with recalls in 2009 and 2010 of about 5 million Toyota and Lexus vehicles with gas pedals that could become entrapped in floor mats.

A high-speed crash involving a Lexus in August 2009 killed four people near San Diego, prompting the government to investigate the recall. After reviewing crash evidence and other data, NHTSA investigators concluded that Toyota failed to notify the government about a known safety defect within five days.

In the second case, Toyota conducted a recall in 2004 of Hilux trucks in Japan with steering relay rods that could break and affect steering. Toyota told US regulators in 2004 that the safety problem was limited to vehicles in Japan.

But a year later, Toyota told NHTSA the steering defect was also found in several US models and recalled nearly 1 million vehicles.