Center City, Philadelphia's engine for growth for the last decade or more, is showing signs of distress, according to statistics compiled by the Center City District for its annual "State of Center City" report.

From office rental rates to visits to tourist attractions and the number of major conventions on the horizon, a variety of measures of the health of the city's core suggest it might not be quite as vibrant as hoped.

For instance, while Center City's population inches higher, office rental rates run stubbornly below national averages, an indication of a city's weakness in attracting new employers.

Employment in health care and education - the city's biggest job creators - has been flattening and, in the first time in a decade, declined in 2013.

Even tourism, a major boom in recent years, is showing unevenness. While total hotel-room nights are up, 10 of the city's 18 most important cultural attractions reported a drop in attendance in 2013. Losers included the Liberty Bell, Independence Hall, and the Philadelphia Museum of Art.

"This is not meant to be a purely promotional report," said Paul Levy, chief executive officer of the Center City District. "This is meant to be a look at our strengths and our challenges. The city is loads better than it was, but it is not yet fulfilling its full potential."

The 75-page report is generally upbeat, highlighting the positive while not hiding the negative. It drives home the importance of Center City to Philadelphia and the challenges both face.

For instance, Greater Center City (Girard Avenue to Tasker Street, river to river) holds 43.3 percent of the city's jobs. It ranks behind only Manhattan in the gross number of downtown residents among major U.S. cities, and experienced a 13 percent increase in residents from 2000 to 2013.

Dig deeper, however, and there are reasons for concern.

Office rental averages show that Philadelphia continues to do a poor job of attracting new employers when compared with other major cities and the region's suburbs.

While Center City's commercial occupancy rate (86 percent) is slightly higher than the national average for central business districts (85.8 percent), the per-square-foot rental rate ($24.67) dramatically trails the national average ($35.19). When it comes to top-tier office space, the Pennsylvania suburbs are commanding a higher rent ($27.95) than Center City ($27.11).

Since 1990, Center City's share of the region's office space has declined from 36.3 percent to 29.1 percent.

Overall, Philadelphia is a laggard in job growth. Between 2012 and 2013, jobs grew 1.57 percent nationwide, 1 percent in the Philadelphia suburbs, and 0.5 percent in the city. That slower growth means an increasing number of Philadelphians (188,000 last year) leave the city each day to work.

Among the largest drivers of city employment are major hospitals and universities. From 2003 to midyear 2012, the number of health-care and higher-education jobs grew steadily from 170,430 to about 199,000. From mid-2012 to mid-2013, however, there was a drop of about 4,500 jobs in the sectors, the only decline in 10 years.

Also down are the number of large conventions set to come to the Convention Center. In 2013, the center attracted eight conventions with attendance of greater than 14,000. Currently, there are none booked for 2014 that exceed 13,000 attendees.

Levy acknowledged the shortcomings, but noted each had its own roots and solutions. The basic core of the city remains a work in progress, he said.